Average Error: 10.5 → 0.2
Time: 12.4s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{1}{y} \cdot \frac{x}{y}\]
\frac{x}{y \cdot y}
↓
\frac{1}{y} \cdot \frac{x}{y}
double f(double x, double y) {
        double r14146889 = x;
        double r14146890 = y;
        double r14146891 = r14146890 * r14146890;
        double r14146892 = r14146889 / r14146891;
        return r14146892;
}
↓
double f(double x, double y) {
        double r14146893 = 1.0;
        double r14146894 = y;
        double r14146895 = r14146893 / r14146894;
        double r14146896 = x;
        double r14146897 = r14146896 / r14146894;
        double r14146898 = r14146895 * r14146897;
        return r14146898;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original10.5
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.5

    \[\frac{x}{y \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}}\]
  4. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{y}}\]

  6. Final simplification0.2

    \[\leadsto \frac{1}{y} \cdot \frac{x}{y}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"

  :herbie-target
  (/ (/ x y) y)

  (/ x (* y y)))